I have used bicycle mode of Google Maps for this purpose. Of course Google maps is not available everywhere. The idea is to use the voice prompts for each turn. You may be able to follow a route created in other software, but I haven't tried that.
I've done it two ways. The first time, I arranged a small pocket, pinned to the upper left of my jersey. It looked somewhat unstylish, so the next few times I put my phone in the back pocket of my jersey. The first way was easier to hear. I didn't want to use an earpiece because it can reduce, as you say, my situational awareness.
There are issues with using Google Maps in this way, so It's important to review the route before you start. Use Street View to check places where the route turns. The main issues I found are
Sometimes it selects a route that is not viable for a bike, even though it supports bicycle mode. Again, Street View can help here. I prefer not to ride with 100kph traffic, or take my road bike on goat trails.
Sometimes the voice prompt is misleading, for example when telling you to "take the fourth exit" from a roundabout. Does that mean a U turn? Or sometimes telling you to turn right, when maybe you need to veer right. And because of GPS device and software limitations, it can sometimes get a bit confused about where you are. Again, reviewing the route helps.
If you hear the navigation voice saying things you don't understand or expect, then stop, get your phone out and see what's going on. The last time I used it I took a wrong turn in a hurry. At first it just said "turn left", but I kept going. When it started saying "make a U turn" I figured it was time to see what it was talking about.
The big advantage is that if you get off your route, it is already working out a new route to get to your destination.
In response a comment: Google maps does have the ability to produce turn-by-turn instructions. You can either print them or view them on your device. I have successfully used this method for 1000km road trips (by car).